Remember Jeremy, his grandpa and the bookcase from an earlier Concept? Well in that Concept, they used the actual bookcase to create a design using a unit scale. Now Jeremy is going to figure out the actual size of a different bookcase using a drawing.Take a look.

Jeremy has a drawing of the bookcase which shows that the bookcase is
inches high. The scale says, 2 inches = 1 foot.

Given this scale, what is the actual height the bookcase?

This Concept will show you how to use unit scale to figure out actual dimensions. We will look at this problem again at the end of the Concept.

Guidance

Sometimes, you will have a scale drawing, map or model to work with first. You won’t be given the actual dimensions. Instead, you will have to use the unit scale that accompanies the scale model, drawing or map to figure out the actual dimensions.

This often happens with maps. You look at a map and try to figure out how far it is from one city to another. The scale in the bottom of the map can help you with this. If the scale says that 1” = 100 miles and the map indicates that there is 4 inches between one city and the next, then you can say that the actual distance between the two cities is 400 miles.

Hector made this scale model of the Statue of Liberty. The scale height of his model, from the base to the torch, is 4.65 centimeters. Find the actual height of the Statue of Liberty.

Write the unit scale as a ratio.

The scale height of the model is 4.65 centimeters. Use
to represent the actual height of the Statue of Liberty.

a smaller drawing that is used to represent a larger, life-size building or model.

Unit Scale

a measurement meant to represent the actual measurements of a larger, life-size building, map or other item. For example 1” = 2 feet would be a unit scale.

Guided Practice

Here is one for you to try on your own.

The map below shows the distances between three towns.

a. On the map, the distance between Smithville and Frankton is
inches. Find the actual straight-line distance between Smithville and Frankton.

b. On the map, the distance between Frankton and Blair is
inches. Find the actual straight-line distance between Frankton and Blair.

c. How many miles closer is Frankton to Blair than to Smithville?

Answer

First, let’s look at the information that we have been given. Then we can use this information to solve each part of the problem. Notice that there are three parts,
and
.

The unit scale is
. Express that ratio as a fraction. Since
, use 0.25 mile as the first term of the ratio.

Now, consider part
.

You know that the scale distance between Smithville and Frankton is
inches. The actual distance between those two towns is unknown, so use
to represent that distance. Write a ratio to represent this. Since
, use 2.25 as the first term.

Set up a proportion using the unit scale and the ratio above and solve for
.

The actual distance between Smithville and Frankton is 18 miles.

Next, consider part
.

You know that the scale distance between Frankton and Blair is
inches. The actual distance between those two towns is unknown, so use
to represent that distance. Write a ratio to represent this. Since
, use 1.5 as the first term.

Set up a proportion using the unit scale and the ratio above and solve for
.

The actual distance between Frankton and Blair is 12 miles.

Finally, consider part
.

We know that Smithville is 18 miles from Frankton, and that Blair is 12 miles from Frankton. So, we can subtract to find out how much closer Frankton is to Blair than to Smithville.